Related papers: Separability Problems in Creative Telescoping
Consider the representations of an algebraic group G. In general, polynomial invariant functions may fail to separate orbits. The invariant subring may not be finitely generated, or the number and complexity of the generators may grow…
High dimensional classification has been highlighted for last two decades and much research has been conducted in order to circumvent challenges encountered in high dimensions. While existing methods have focused mainly on developing…
The separation problem for a class Q of database queries is to find a query in Q that distinguishes between a given set of `positive' and `negative' data examples. Separation provides explanations of examples and underpins the…
In 2012 Chen and Singer introduced the notion of discrete residues for rational functions as a complete obstruction to rational summability. More explicitly, for a given rational function f(x), there exists a rational function g(x) such…
A new criterion, based on noncontextuality, is derived to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. An experiment is proposed to test the violation of noncontextuality…
The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical…
In this paper, some classes of discrete functions of $k$-valued logic are considered, that depend on sets of their variables in a particular way. Obtained results allow to "construct" these functions and to present them in their tabular,…
Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks…
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…
We consider the problem of reconstructing binary images from their horizontal and vertical projections. We present a condition that the projections must necessarily satisfy when there exist two disjoint reconstructions from those…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
The success of present and future cosmological studies is tied to the ability to detect discrepancies in complex data sets within the framework of a cosmological model. Tensions caused by the presence of unknown systematic effects need to…
Most automated verifiers for separation logic target the symbolic-heap fragment, disallowing both the magic-wand operator and the application of classical Boolean operators to spatial formulas. This is not surprising, as support for the…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
Conditions for the unique solvability of the Cauchy problem for a family of scalar functional differential equations are obtained. These conditions are sufficient for the solvability of the Cauchy problem for every equation from the family…
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite…
Firstly, we reduce the long-standing problem of ascertaining the Hilbert-Schmidt probability that a generic pair of qubits is separable to that of determining the specific nature of a one-dimensional (separability) function of the radial…
Reproducibility is a confused terminology. In this paper, I take a fundamental view on reproducibility rooted in the scientific method. The scientific method is analysed and characterised in order to develop the terminology required to…
I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide…
In the photonic design problem, a scientist or engineer chooses the physical parameters of a device to best match some desired device behavior. Many instances of the photonic design problem can be naturally stated as a mathematical…